Involving the Solubility-Product Constant

In Chapters 17 and 18, we described two types of equilibrium problems. In one type, we use concentrations to find K, and in the other, we use K to find concentrations. Here we encounter the same two types. 

Determining fCjp from Solubility The solubilities of ionic compounds are determined experimentally, and several chemical handbooks tabulate them. Most solubility values are given in units of grams of solute dissolved in 100 grams of H2O. Because the mass of compound in solution is small, a negligible error is introduced if we assume that TOO g of water is equal to 100 mL of solution. We then convert the solubility from grams of solute per 100 mL of solution to molar solubility, the amount (mol) of solute dissolved per liter of solution (that is, the molarity of the solute). Next, we use the equation for the dissolution of the solute to find the molarity of each ion and substitute into the ion-product expression to find the value of K p. 

Problem (a) Lead(II) sulfate (PbS04) is a key component in lead-acid car batteries. Its solubility in water at 25°C is 4.25X10 g/100 mL solution. What is the ATjp of PbS04  

Plan We are given the solubilities in various units and must find K p. Por each compound, we write an equation for its dissolution to see the number of moles of each ion, and then write the ion-product expression. We convert the solubility to molar solubility, find the molarity of each ion, and substitute into the ion-product expression to calculate K p. Solution (a) Por PbS04. Writing the equation and ion-product (K p) expression  

Check The low solubilities are consistent with A p values being small. In (a), the molar 

Determining molarities of the ions I mol of Pb and 2 mol of F form when 1 mol of PbpT dissolves, so we have 

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It is imperative that you understand these ideas involving the solubility product constant.Let s look at another example. One mole of aluminum hydroxide [Al(OH)j] gives one mole of aluminum ions and three moles of hydroxide ions in solution. 

The Ion-Product Expression (2sp) and the Solubility-Product Constant (kfsp) 634 Calculations Involving the Solubility-Product Constant 635 Effect of a Common Ion on Solubility 637... 

When solving common-ion-effect problems, calculations like the ones above involving finding concentrations and Ksp s can still be done, but the concentration of the additional common ion will have to be inserted into the solubility product constant expression. Sometimes, if the Ksp is very small and the common ion concentration is large, we can simply approximate the concentration of the common ion by the concentration of the ion added. 

When written in this form, to involve only the product of the concentrations of the ions, the constant KSi, is called the "solubility-product constant."... 

The foregoing example illustrates how equilibrium constants for overall cell reactions can be determined electrochemically. Although the example dealt with redox equilibrium, related procedures can be used to measure the solubility product constants of sparingly soluble ionic compounds or the ionization constants of weak acids and bases. Suppose that the solubility product constant of AgCl is to be determined by means of an electrochemical cell. One half-cell contains solid AgCl and Ag metal in equilibrium with a known concentration of CP (aq) (established with 0.00100 M NaCl, for example) so that an unknown but definite concentration of Kg aq) is present. A silver electrode is used so that the half-cell reaction involved is either the reduction of Ag (aq) or the oxidation of Ag. This is, in effect, an Ag" Ag half-cell whose potential is to be determined. The second half-cell can be any whose potential is accurately known, and its choice is a matter of convenience. In the following example, the second half-cell is a standard H30" H2 half-cell. 

The solubility product constant may be determined by direct measnrements or calcnlated from the standard Gibbs free energies of formation (JsGf) of the species involved at their standard states. For the reaction scheme (Equation 8.13) the Gibbs free energy change is ... 

The Solubility-Product Constant (Ksp) Calculations Involving Ksp The Effect of a Common Ion The Effect of pH Qsp rs. K ... 

As with any equilibrium, the extent to which this dissolution reaction occurs is expressed by the magnitude of its equilibrium constant. Because fliis equilibrium equation describes the dissolution of a solid, the equilibrium constant indicates how soluble tire solid is in water and is referred to as the solubility-product constant (or simply tire solubility product). It is denoted Kgp, where sp stands for solubility product. The equilibrium-constant expression for this process is written according to tire same rules as those that apply to any equilibrium-constant expression. That is, Ihe concentration terms of the products are multiplied togefli-er, and each is raised to the power of its stoichiometric coefficient in the balanced chemical equation, and these are divided by the concentration terms of the reactants multiplied together, and each raised to the power of its stoichiometric coefficient. Solids, liquids, and solvents do not appear in the equilibrium-constant expressions for heterogeneous equilibria (Section 15.3), however, so the solubility product equals the product of the concentration (f the ions involved in the equilibrium, each raised to the poioercfits coefficient in the equilibrium equation. Thus, the solubility-product expression for the equilibrium expressed in Equation 17.15 is... 

In equilibria that involve slightly soluble compounds in water, the equilibrium constant is called the solubility product constant, The activity of the pure solid BaS04 is one... 

The solubility product constant is a useful parameter for calculating the aqueous solubility of sparingly soluble compounds under various conditions. It maybe determined by direct measurement or calculated from the standard Gibbs energies of formation AjG° of the species involved at their standard states. Thus if = [M+] , [A ]" is the equilibrium constant for the reaction... 

Is there a relationship between the solubility product constant, K p, of a solute and the solute s molar solubility—its molarity in a saturated aqueous solution As shown in Examples 18-2 and 18-3, there is a definite relationship between them. As discussed in Section 18-4, calculations involving Kgp are generally more subject to error than are those involving other equilibrium constants, but the results are suitable for many purposes. In Example 18-2, we start with an experimentally determined solubility and obtain a value of Xgp. 

In the precipitation reaction involving chloride and silver nitrate, the addition of even a small quantity of the latter shall effect precipitation of AgCl provided that Ksp has been exceeded significantly. At this juncture, the concentrations of both Ag+ and Cl are related by the solubility-product equilibrium constant thus, we have ... 

CIDT is a hybrid process involving selective crystallizahon of desired diastereomer and in situ epimerizahon of undesired diastereomer. Figure 9.6 illustrates the system, in which two solid diastereomers. A, and B can equilibrate with each other via their dissolved counterparts Aj and B,. The solubility products of A and B are given by = [AJ and Ig = [BJ, and the equilibrium constant for A and B in solu-hon is given by K = [BJ/[AJ. For L K > Lg at a temperature below their melting points, the mixture of A, and B, should eventually be transformed into pure Bj, in other words, CIDT occurs [14a]. 

The zero-point G0 depends on the solvent and conceivably on other variables. Thus, the distribution coefficient K between two phases correspond to the species being exp[(< oi — G02)/RT] times more soluble in the phase 2 than in the phase 1. The solubility product Ksp is an expression of G0 in the solid compared with G0 in the solution, if we accept to speak about free energies of ions and not only of neutral species. Since Arrhenius convinced his reluctant contemporaries about the predominant (or complete) dissociation of salts in aqueous solution, it became acceptable to write complex formation constants involving concentrations of ions and not only of neutral molecules. 

The model balance equation for each metal and ligand (e.g., Eqs. 2.49 and 2.52) is augmented to include formally the concentration of each possible solid phase. By choosing an appropriate linear combination of these equations, it is always possible to eliminate the concentrations of the solid phases from the set of equations to be solved numerically. Moreover, some of the free ionic concentrations of the metals and ligands also can be eliminated from the equations because of the constraints imposed by on their activities (combine Eqs. 3.2 and 3.3), which holds for each solid phase formed. The final set of nonlinear algebraic equations obtained from this elimination process will involve only independent free ionic concentrations, as well as conditional stability and solubility product constants. The numerical solution of these equations then proceeds much like the iteration scheme outlined in Section 2.4 for the case where only complexation reactions were considered, with the exception of an added requirement of self-consistency, that the calculated concentration of each solid formed be a positive number and that IAP not be greater than Kso (see Fig. 

Strictly, K should be written in terms of thermodynamic activities and not concentrations, but activities can be replaced by concentrations (denoted by square brackets) because of the low solubilities involved (see section 3.3.1). At samration the concentration of the crystalline silver chloride [AgClJ is essentially constant and the solubility product, may... 

Skill 9.3 Solving problems involving solubility product constants of slightly soluble salts and the common-ion effect... 

It may also be argued that the simulation of water-rock interactions should allow for solubility equilibria involving feldspars, micas, etc. For such studies the choice of solublity product constants and free energies must and should be made by the investigators. We cannot propose such values here when an enormous range of values and properties (solid-solutions, interlayering, defects, surface areas, etc.) is known to exist for these minerals and reversible solubility behavior has not been demonstrated. 

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